Developments of fuzzy PID controllers

Abstract: This paper describes the development and tuning methods for a novel self-organizing fuzzy proportional integral derivative (PID) controller. Before applying fuzzy logic, the PID gains are tuned using a conventional tuning method. At supervisory level, fuzzy logic readjusts the PID gains online. In the first tuning method, fuzzy logic at the supervisory level readjusts the three PID gains during the system operation. In the second tuning method, fuzzy logic only readjusts the proportional PID gain, and the corresponding integral and derivative gains are readjusted using the Ziegler–Nichols tuning method while the system is in operation. For the compositional rule of inferences in the fuzzy PID and the self-organizing fuzzy PID schemes two new approaches are introduced: the min implication function with the mean of maxima defuzzification method, and the max-product implication function with the centre of gravity defuzzification method. The fuzzy PID controller, the self-organizing fuzzy PID controller and the PID controller are all applied to a non-linear revolute-joint robot arm for step input and path tracking experiments using computer simulation. For the step input and path tracking experiments, the novel self-organizing fuzzy PID controller produces a better output response than the fuzzy PID controller; and in turn both controllers exhibit better process output than the PID controller.     

基于积分时滞系统史密斯预估器的研究

在积分时滞系统(IPDT)中,传统的史密斯预估器不能很好的消除稳态误差,而且在模型失配时易产生欠补偿问题.为此,文中提出了改进型的史密斯预估器,首先利用反馈控制器,将实际过程与模型过程的误差反馈到控制信号端.其次,在控制对象端加上串联控制器和反馈补偿控制器,分别采用不同的方法进行设计,以消除扰动对系统的影响. MATLAB仿真结果显示,系统具有较好的输出响应,能够有效消除扰动误差.     

关于模糊PID控制器推理机维数的研究

对一维(1D)至三维(3D)模糊PID控制器进行了系统的分析研究,提出了四项系统功能特性指标来评价不同结构的控制器;这包括控制分量合成,耦合影响,增益相关和规则增长.通过对最常见的二维Mamdani模糊控制器进行分析研究,发现该控制器存在功能缺陷.为此,提出了最优结构的一维模糊PID控制器.该控制器采用了"1D-3D"映射关系的模糊推理机,从而实现了三个控制分量可以独立不相关的调整功能.通过与二维和三维控制器比较结果表明,一维控制器具有最佳系统功能特性.     

Output Tracking Control of a Hydrogen-air PEM Fuel Cell

Hydrogen-air proton exchange membrane (PEM) fuel cell is a promising clean energy. However, the stack output tracking control is still a challenging problem due to the soft characteristic of the stack. Both over-and less-control will cause the stack flooding or oxygen lacking which dramatically decreases the life of stacks. Traditional control methods rely on the accurate model of the fuel cell system, which is a high-order nonlinear system, and involve a complex controller design process. This paper combines the data-based fuzzy cluster modeling technology with the sliding mode control and the integral actions. The sliding mode controller tracks the dynamic changes of the fuel cell system and the integral controller eliminates the steady-state errors. Simulation results demonstrate good performance of the proposed control method.      

Some investigations on fuzzy P + fuzzy I + fuzzy D controller for non-stationary process

The paper addresses the adaptive behaviour of parallel fuzzy proportional plus fuzzy integral plus fuzzy derivative (FP+FI+FD) controller. The parallel FP+FI+FD controller is actually a non-linear adaptive controller whose gain changes continuously with output of the process under control. Two non-stationary processes, whose characteristics change with time, are considered for simulation study. Simulation is performed using software LabVIEW TM . The set-point tracking response of parallel FP+FI+FD is compared with conventional parallel proportional plus integral plus derivative (PID) controller, tuned with the Ziegler-Nichols (Z-N) tuning technique. Simulation results show that conventional PID controller fails to track the set-point and becomes unstable as the process changes its characteristic with time. But the parallel FP+FI+FD controller shows considerably much better set-point tracking response and does not deviate from steady state. Also, a huge spike is observed in the output of PID controller as the reference set-point and process parameters are changed, while the FP+FI+FD controller gives spike free control signal.     

Multi‐objective robust fuzzy fractional order proportional–integral–derivative controller design for nonlinear hydraulic turbine governing system using evolutionary computation techniques

The present paper proposes a novel multi‐objective robust fuzzy fractional order proportional–integral–derivative (PID) controller design for nonlinear hydraulic turbine governing system (HTGS) by using evolutionary computation techniques. The fuzzy fractional order PID (FOPID) controller takes closed loop error and its fractional derivative as inputs and performs fuzzy logic operations. Then, it produces the output through the fractional order integrator. The predominant advantages of the proposed controller are its capability to handle complex nonlinear processes like HTGS in heuristic manner, due to fuzzy incorporation and extending an additional flexibility in tuning the order of fractional derivative/integral terms to enhance the closed loop performance. The present work formulates the optimal tuning problem of fuzzy FOPID controller for HTGS as a multi‐objective one instead of a traditional single‐objective one towards satisfying the conflicting criteria such as less settling time and minimum damped oscillations simultaneously to ensure the improved dynamic performance of HTGS. The multi‐objective evolutionary computation techniques such as non‐dominated sorting genetic algorithm‐II (NSGA‐II) and modified NSGA‐II have been utilized to find the optimal input/output scaling factors of the proposed controller along with the order of fractional derivative/integral terms for HTGS system under no load and load turbulence conditions. The performance of the proposed fuzzy FOPID controller is compared with PID and FOPID controllers. The simulations have been conducted to test the tracking capability and robust performance of HTGS during dynamic set point changes for a wide range of operating conditions and model parameter variations, respectively. The proposed robust fuzzy FOPID controller has ensured better fitness value and better time domain specifications than the PID and FOPID controllers, during optimization towards satisfying the conflicting objectives such as less settling time and minimum damped oscillations simultaneously, due to its special inheritance of fuzzy and FOPID properties.     

基于模糊控制器的炉温控制算法仿真与应用

针对电阻炉数学模型时变的特点,提出了一种带积分输出的模糊控制器设计方案.以带积分输出的模糊控制算法为基础,对实验室电阻炉的炉温控制装置进行了软件设计,并以西门子S7-200可编程控制器为平台,采用组态王监控系统软件对控制算法进行了调试.Matlab仿真结果表明,带积分输出的模糊算法能够较好地适应数学模型时变的控制对象,得到满意的控制效果.     

基于遗传算法的P-F-PI控制器在机器人手臂定位控制中的应用

提出用遗传算法来优化控制参数的P F PI(比例 模糊 比例积分 )控制器 ,控制机器人手臂定位系统 .P F PI控制器是在大偏差时用比例控制 ,在中偏差时用F控制 ,接近稳态时用PI控制 ,而这三个控制器的切换参数以及F控制器中的修正系数用遗传算法来优化 .实验证明 ,该控制方法能满足机器人手臂定位控制动态和静态要求 .     

A fuzzy logic based supervisory hierarchical control scheme for real time pressure control

This paper describes a supervisory hierarchical fuzzy controller （SHFC） for regulating pressure in a real-time pilot pressure control system. The input scaling factor tuning of a direct expert controller is made using the error and process input parameters in a closed loop system in order to obtain better controller performance for set-point change and load disturbances. This on-line tuning method reduces operator involvement and enhances the controller performance to a wide operating range. The hierarchical control scheme consists of an intelligent upper level supervisory fuzzy controller and a lower level direct fuzzy controller. The upper level controller provides a mechanism to the main goal of the system and the lower level controller delivers the solutions to a particular situation. The control algorithm for the proposed scheme has been developed and tested using an ARM7 microcontroller-based embedded target board for a nonlinear pressure process having dead time. To demonstrate the effectiveness, the results of the proposed hierarchical controller, fuzzy controller and conventional proportional-integral （PI） controller are analyzed. The results prove that the SHFC performance is better in terms of stability and robustness than the conventional control methods.     

板料拉深成形液压系统模糊控制建模

针对板料拉深成形系统中的变压边力液压控制动态性能和稳态精度较差的难题,建立了一个基于模糊PID自适应调整的液压模糊控制模型,并借助MATLAB仿真得到了控制参数的优化模糊查询表．最后结合实际板料拉深成形系统,选取两种变压边力加载模式进行实时变压边力模糊控制应用效果验证．应用结果表明:采用模糊PID自适应控制方式可大大改善拉深成形液压控制系统的动态响应性能和稳态精度．当压边力输入曲线为4吨的阶跃信号,模糊控制下系统的最大超调量仅为理想设定值的4．25％,大大小于原来无PID控制时的21．24％及常规PID控制下的31．07％,且达到稳定状态的调节高度也大大缩小,仅略为5 mm左右,调节时间略为0．24 s;而当输入为U型变压边力加载曲线时,系统的最大超调量比原来无PID控制时下降了约5％,且达到稳态时的调节高度也缩短了约1 mm左右,使整个拉深变压边力系统的动态性能和稳态精度得到了有效的提高．     

基于解析结构的模糊控制器的稳定性和一致逼近性分析

基于模糊控制的解析结构理论,设计了输入变量采用三角形、全交迭,等差间距分布的隶属函数,输出变量采用对称、均匀分布的单点隶属函数和线性控制规则的二维模糊控制器,推导了模糊控制器的解析表达式。利用Lyapunov第二法论证了该模糊控制系统在平衡点处的局部稳定性,并证明了模糊控制器的一致逼近性。     

无模型控制律的一种改进算法

针对基本形式的无模型控制律没有充分利用输入输出数据包含的信息,利用输入输出数据的高阶信息,提出了一种新的控制准则函数,推导了其控制律算法.然后针对一类具有积分环节的被控对象设计了带反馈环节的无模型控制器.并在相同条件下,对分别采用基本算法和改进算法设计的无模型控制器进行控制性能仿真研究.仿真结果表明:改进的无模型控制律算法表现出优良的控制品质,跟踪性能良好,具有参数自适应性.该算法适合处理参数时变、结构时变的非线性系统的控制问题.     

永磁直线同步电机位置系统的模糊IP控制研究

针对具有电磁推力大、响应快、易于矢量解耦控制的永磁直线同步电机PMLSM,研究高精度位置伺服控制系统的设计,以满足高速加工与高精度微进给加工的需求;考虑被控对象的变化和外界扰动,控制器的参数难于在线修订,设计了一种模糊/积分-比例IP位置控制器;它将具有并联反馈环节的IP控制器与模糊控制器有效结合,根据位置偏差的变化率进行切换,即存在较大输入指令与系统输出偏差较大时采用模糊控制,而系统输出接近于输入指令时则采用IP控制器,从而发挥模糊控制器对变参数系统的自适应性和IP控制器的快速和准确性优势;仿真实验结果表明模糊/IP控制器在稳态精度和动态性能方面优于单纯的IP控制器和模糊控制器,能够满足变参数控制系统的性能指标。     

模糊控制器的结构化分析及系统化设计方法

对于模糊控制器的输入变量,采用一种新型的不均匀、全交迭、三角形的隶属度函数,推导了两输入（e,△e)－输出（△u）的典型模糊控制器输出的解析表达式,并对最常用的输入变量各取5个模糊变量的情况进行分析。在此基础上提出一种模糊控制系统的系统化设计方法,可根据已有的PI／PD控制器参数设计相应的模糊控制器参数。仿真实验说明了该方法的有效性。     

Dynamic output feedback control with output quantizer for nonlinear uncertain T‐S fuzzy systems with multiple time‐varying input delays and unmatched disturbances

The dynamic output feedback control problem with output quantizer is investigated for a class of nonlinear uncertain Takagi‐Sugeno (T‐S) fuzzy systems with multiple time‐varying input delays and unmatched disturbances. The T‐S fuzzy model is employed to approximate the nonlinear uncertain system, and the output space is partitioned into operating regions and interpolation regions based on the structural information in the fuzzy rules. The output quantizer is introduced for the controller design, and the dynamic output feedback controller with output quantizer is constructed based on the T‐S fuzzy model. Stability conditions in the form of linear matrix inequalities are derived by introducing the S‐procedure, such that the closed‐loop system is stable and the solutions converge to a ball. The control design conditions are relaxed and design flexibility is enhanced because of the developed controller. By introducing the output‐space partition method and S‐procedure, the unmatched regions between the system plant and the controller caused by the quantization errors can be solved in the control design. Finally, simulations are given to verify the effectiveness of the proposed method.     

模糊控制器输出值不变的两个充分条件

模糊控制器通常由模糊化、模糊推理以及清晰化三部分构成, 而模糊推理决定了一个由输入论域到输出论域的模糊映射. 当模糊映射为常值映射时, 任意选择模糊化和去模糊化方式, 模糊控制器的输出值不因输入信号变化而改变. 本文给出了模糊映射为常值映射的两个充分条件, 并将结论从单入单出模糊系统推广到多入单出模糊系统.     

Improved Image Based Visual Servoing with Parallel Robot

The position regulation problem of an eye-in-hand type of parallel robot based pointing systems (PRBPS) is considered in this paper. A fuzzy logic system is first designed to compensate for the uncertainties of the parallel robot and the uncertainty of the image Jacobian, then a hybrid controller (HC) including the image-based nonlinear controller and the adaptive supervisory fuzzy logic controller (ASFLC) is derived by using the Lyapunov direct method to realize the position regulation (PR). The stability of the closed-loop system in the Lyapunov sense is proven theoretically. The fuzzy scaling matrix is combined with the HC to improve the performance of the control system. The simulation results demonstrate that the PRBPS realizes PR with very good robustness to the parameter uncertainties, and the control input torques and settling time are reduce greatly in the case of large initial feature errors.     

一种简化的三维模糊制器

针对三维模糊控制器规则多,结构复杂,难以实现的问题,提出了一种简化的三维模糊控制器。该方法是把三个输入量分别为偏差、偏差变化、偏差的偏差变化的一维模糊控制器加权融合实现简化的三维模糊控制器。并提出了根据不同类型的被控对象设置三个加权系数。加权系数具有粗调、细调和微调的作用,类似于传统PID调节器的比例、积分和微分,实现对系统静差的消除。     

Design and Robust Performance Evaluation of a Fractional Order PID Controller Applied to a DC Motor

This paper proposes a methodology for the quantitative robustness evaluation of PID controllers employed in a DC motor. The robustness analysis is performed employing a 23 factorial experimental design for a fractional order proportional integral and derivative controller (FOPID), integer order proportional integral and derivative controller (IOPID) and the Skogestad internal model control controller (SIMC). The factors assumed in experiment are the presence of random noise, external disturbances in the system input and variable load. As output variables, the experimental design employs the system step response and the controller action. Practical implementation of FOPID and IOPID controllers uses the MATLAB stateflow toolbox and a NI data acquisition system. Results of the robustness analysis show that the FOPID controller has a better performance and robust stability against the experiment factors.      

基于模糊PI的永磁同步电机矢量控制

针对永磁同步电机矢量控制系统中,传统PID控制器对永磁同步电机控制性能效率不高以及对工作环境变化的适应性能不良等问题,首先,在两相旋转坐标系下采取双轴理论建立永磁同步电机数学模型;接着,采用模糊控制理论对永磁同步电机矢量控制系统中转速环传统的普通PID控制器进行改进研究,深入地从理论层次研究分析建立得到模糊PI控制器....